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Is there some particular order here? We've got some seriously spiffy calligraphy on the wall at our dojo but I don't know whether its supposed to go right to left or left to right.

Usually it goes triangle circle square - Ueshiba uses that order in Take Musu Aiki, IIRC. Left to right or right to left, it doesn't make much difference, though most modern Japanese tends to be written left to right.

In Tsubaki America's haiden (if I'm recalling correctly) there is a picture of triangle circle and square which goes left to right, respectively. On the web page it also is shown in that format. I can see how it might go right to left given the direction of Japanese writing, but I couldn't say very well. Considering as a group they seem to represent a kind of unitary principle, I can see how there might not always be a fixed order. Looking at the physical symbolism of gas, liquid, and solid, depending on whether you're warming up or cooling down, you move from one "direction" to another, for example.
Hopefully people with a better understanding will be able to shed a more definate light on the subject...oops didn't see Chris's post when I started this: there ya go.

Usually it goes triangle circle square - Ueshiba uses that order in Take Musu Aiki, IIRC. Left to right or right to left, it doesn't make much difference, though most modern Japanese tends to be written left to right.

Best,

Chris

Well I don't think calligraphy and modern Japanese are entirely unified sets.

No, but if you see most calligraphy these days it tends to go right to left. Why not? It's what most people are used to seeing and writing.

It's not a rule, though, you still see left to right here and there.

Best,

Chris

When the brushes come out, its pretty much right to left, top to bottom.Though the kanji themselves tend to go top to bottom, left to right. And of course all rules that cover anything in Japanese are 100% absolute, except for the exceptions.